Domain and Range: Quadratic

Front

What is the definition of the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the definition of the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, represented as (-∞, ∞).

Front

What is the range of a quadratic function that opens upwards?

Back

The range is from the vertex's y-coordinate to positive infinity, expressed as [k, ∞) where k is the minimum value.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is from negative infinity to the vertex's y-coordinate, expressed as (-∞, k] where k is the maximum value.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) for a quadratic in the form y = ax^2 + bx + c.

Front

Back

The vertex is at the point (2, -3) after calculating x = 2 and substituting back into the function.

Front

What does it mean for a function to be 'one-to-one'?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

How do you determine the range of a quadratic function given its vertex?

Back

If the vertex is the minimum point, the range is [k, ∞); if it's the maximum point, the range is (-∞, k].